We investigate the amount of noise required to turn a universal quantum gate set into one that can be efficiently modeled classically. This question is useful for providing upper bounds on fault-tolerant thresholds, and for understanding the nature of the quantum-classical computational transition. We refine some previously known upper bounds using two different strategies. The first one involves the introduction of bientangling operations, a class of classically simulable machines that can generate at most bipartite entanglement. Using this class we show that it is possible to sharpen previously obtained upper bounds in certain cases. As an example, we show that under depolarizing noise on the controlled-NOT gate, the previously known upper bound of 74% can be sharpened to around 67%. Another interesting consequence is that measurement-based schemes cannot work using only two-qubit nondegenerate projections. In the second strand of the work we utilize the Gottesman-Knill theorem on the classically efficient simulation of Clifford group operations. The bounds attained using this approach for the $\pi ∕8$ gate can be as low as 15% for general single-gate noise, and 30% for dephasing noise.

It is well known that entangled quantum states are nonlocal: the corrrelations between local measurements carried out on these states cannot be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are more nonlocal than bipartite ones in the sense that even some nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely, we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalizes work of Svetlichny and others in which it was showed that a particular class of classical nonlocal models, the “separable” models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition.

Using the Oak Ridge National Laboratory ion-atom merged-beams apparatus, absolute total charge-transfer cross sections have been measured for collisions of ${\mathrm{He}}^{2+}+\mathrm{H}$ over a range of energies from $380\text{to}2620\mathrm{eV}∕\mathrm{u}$. The experimental results are compared to previous measurements using different experimental techniques. A hidden-crossing coupled-channel (HCCC) calculation is performed in the collision energy range of $10\text{to}3000\mathrm{eV}∕\mathrm{u}$ and is compared with the measured data as well as with other theories. The HCCC calculation, which is deemed accurate below $1000\mathrm{eV}∕\mathrm{u}$, is also used to determine differential cross sections. The resultant angular scattering information is used to correct the merged-beams data, which is characterized by a large but limited angular acceptance at these collision energies. Our combined experimental and theoretical study provides an improved benchmark for this fundamental system.

We report an optical dipole trap for calcium. The trap is created by focusing a $488\text{−}\mathrm{nm}$ argon-ion laser beam into a calcium magneto-optical trap. The argon-ion laser photoionizes atoms in the trap because of a near-resonance with the $4s4f{}^{1}F_3$ level. By measuring the dipole-trap decay rate as a function of argon-ion laser intensity, we determine the ${}^{1}F_3$ photoionization cross section at our wavelength to be approximately $230\mathrm{Mb}$.

Propagation of a short pulse in an amplifier with excited-state absorption (ESA) is considered. As is shown both analytically and numerically, if the stimulated emission cross section exceeds the ESA cross section, a steady-state pulse of a dissipative soliton type can exist. The parameters of the soliton, i.e., its width, amplitude, and velocity, are calculated. In the opposite case, amplification is inhibited unless ESA is suppressed using an additional control field applied to a transition adjacent to the ESA one [Phys. Rev. A 70, 043801 (2004)]. Propagation and amplification dynamics of a probe pulse in the presence of a strong control field is analyzed. In the limit of a continuous wave control field, a dissipative soliton solution forms, which is a pair of pulses similar to adiabatons. In the case of a pulsed control field, amplification of the probe pulse is transient. Conditions for optimal amplification are derived. Estimates of soliton parameters are made for rare-earth and transition-metal ion-activated laser crystals.

We have studied dark resonances in a thermal gas of rubidium atoms using a variable angle between the two driving optical beams. The inclined angle was tuned between a Doppler-free situation (i.e., collinear beams) and near ${10}^{-3}\mathrm{rad}$, yielding an effective Doppler sensitivity of a far-infrared photon. For the case of buffer gas cells, Dicke narrowing occurs. We can carefully control the transition between the Dicke regime, in which the Doppler broadening is suppressed, and the Doppler-broadened regime, in which the thermal atomic motion strongly couples to the three-level atoms.

An entanglement concentration scheme for unknown atomic entanglement states is proposed via entanglement swapping in cavity QED. Because the interaction used here is a large-detuned one between two driven atoms and a quantized cavity mode, the effects of the cavity decay and thermal field have been eliminated. These advantages can warrant the experimental feasibility of the current scheme.

A method for measuring an integral of a classical field via local interaction of a single quantum particle in a superposition of $2^N$ states is presented. The method is as efficient as a quantum method with $N$ qubits passing through the field one at a time and it is exponentially better than any known classical method that uses $N$ bits passing through the field one at a time. A related method for searching a string with a quantum particle is proposed.

We present an ab initio (quasirelativistic) two-component approach to the computation of molecular parity-violating effects which is based on the zeroth-order regular approximation (ZORA). As a first application, we compute the parity-violating energy differences between various $P$ and $M$ conformations of $C_2$-symmetric molecules belonging to the series ${\mathrm{H}}_2{\mathrm{X}}_2$ with $\mathrm{X}=\mathrm{O}$, S, Se, Te, Po. The results are compared to previously reported (relativistic) four-component Dirac-Hartree-Fock-Coulomb (DHFC) data. Relative deviations between ZORA and DHFC values are well below 2% for diselane and the heavier homologs whereas somewhat larger relative deviations are observed for the lighter homologs. The larger deviations for lighter systems are attributed to the (nonlocal) exchange terms coupling large and small components, which have been neglected in the present ZORA implementation. For heavier systems these play a minor role, which explains the good performance of the ZORA approach. An excellent performance, even for lighter systems, is expected for a related density-functional-theory-based ZORA because then the exchange terms coupling large and small components are absent.

We investigate cluster states of qubits with respect to their nonlocal properties. We demonstrate that a Greenberger-Horne-Zeilinger (GHZ) argument holds for any cluster state: more precisely, it holds for any partial, thence mixed, state of a small number of connected qubits (five, in the case of one-dimensional lattices). In addition, we derive a Bell inequality that is maximally violated by the four-qubit cluster state and is not violated by the four-qubit GHZ state.

We consider an arbitrary continuous-variable three-party Gaussian quantum state which is used to perform quantum teleportation of a pure Gaussian state between two of the parties (Alice and Bob). In turn, the third party (Charlie) can condition the process by means of local operations and classical communication. We find the best measurement that Charlie can implement on his own mode that preserves the Gaussian character of the three-mode state and optimizes the teleportation fidelity between Alice and Bob.

We present an extension of the $T$-matrix approach to scattering of light by a three-level system, using a description based on a Master equation. More particularly, we apply our formalism to calculate the $T$ matrix of a pumped three-level atom, providing an exact and analytical expression describing the influence of a pump on the light-scattering properties of an atomic three-level system.

Triangular symmetric molecules with mirror symmetry perpendicular to the threefold axis are forbidden to have a fixed electrical dipole moment. However, if the ground state is orbitally degenerate and lacks inversion symmetry, then a “quantum” dipole moment does exist. The system of three electrons in $D_{3h}$ symmetry is our example. This system is realized in triatomic molecules like ${\mathrm{Na}}_3$. Unlike the fixed dipole of a molecule like water, the quantum moment does not point in a fixed direction, but lies in the plane of the molecule and takes quantized values $\pm {\mu }_0$ along any direction of measurement in the plane. An electric field $\vec{F}$ in the plane leads to a linear Stark splitting $\pm {\mu }_0\mid \vec{F}\mid$. We introduce a toy model to study the effect of Jahn-Teller distortions on the quantum dipole moment. We find that the quantum dipole property survives when the dynamic Jahn-Teller effect is included if the distortion of the molecule is small. Linear Stark splittings are suppressed in low fields by molecular rotation, just as the linear Stark shift of water is suppressed, but will be revealed in moderately large applied fields and low temperatures. Coulomb correlations also give a partial suppression.

Optical parametric process occurring in a nonlinear planar waveguide can serve as a source of light with nonclassical properties. The properties of the generated fields are substantially modified by scattering of the nonlinearly interacting fields in a photonic-band-gap structure inside the waveguide. A general quantum model of linear operator amplitude corrections to the amplitude mean values and its numerical analysis provide conditions for efficient squeezed-light generation as well as generation of light with sub-Poissonian photon-number statistics. The destructive influence of phase mismatch of the nonlinear interaction can fully be compensated using a suitable photonic-band-gap structure inside the waveguide. Also an increase of the signal-to-noise ratio of the incident optical field can be reached in the waveguide.

The two-loop self-energy correction is evaluated to all orders in $Z\alpha$ for the ground-state Lamb shift of H-like ions with $Z⩾10$, where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant. The results obtained are compared with the analytical values for the $Z\alpha$-expansion coefficients. An extrapolation of the all-order numerical results to $Z=1$ is presented and implications of our calculation for the hydrogen Lamb shift are discussed.

We present detailed numerical calculations of the mechanical torque induced by quantum fluctuations on two parallel birefringent plates with in-plane optical anisotropy, separated by either vacuum or a liquid (ethanol). The torque is found to vary as $\sin \left(2\theta \right)$, where $\theta$ represents the angle between the two optical axes, and its magnitude rapidly increases with decreasing plate separation $d$. For a $40\mu \mathrm{m}$ diameter disk, made out of either quartz or calcite, kept parallel to a barium titanate plate at $d\simeq 100\mathrm{nm}$, the maximum torque (at $\theta =\pi ∕4$) is of the order of $\simeq {10}^{-19}\mathrm{N}\mathrm{m}$. We propose an experiment to observe this torque when the barium titanate plate is immersed in ethanol and the other birefringent disk is placed on top of it. In this case the retarded van der Waals (or Casimir-Lifshitz) force between the two birefringent slabs is repulsive. The disk would float parallel to the plate at a distance where its net weight is counterbalanced by the retarded van der Waals repulsion, free to rotate in response to very small driving torques.

The effects of incoherence and decoherence in a double-slit experiment are studied using both optical and quantum-phenomenological models. The results are compared with experimental data obtained with cold neutrons.

We employ an approach wherein the ground state entanglement of a relativistic free scalar field is directly probed in a controlled manner. The approach consists of having a pair of initially nonentangled detectors locally interact with the vacuum for a finite duration $T$, such that the two detectors remain causally disconnected, and then analyzing the resulting detector mixed state. We show that the correlations between arbitrarily far-apart regions of the vacuum cannot be reproduced by a local hidden-variable model, and that as a function of the distance $L$ between the regions, the entanglement decreases at a slower rate than $\sim \exp [-{(L∕cT)}^3]$.

The theoretically tolerable erasure error rate for scalable quantum computing is shown to be well above 0.1, given standard scalability assumptions. This bound is obtained by implementing computations with generic stabilizer code teleportation steps that combine the necessary operations with error correction. An interesting consequence of the technique is that the only errors that affect the maximum tolerable error rate are storage and Bell measurement errors. If storage errors are negligible, then any detected Bell measurement error below is permissible. For practical computation with high detected error rates, the implementation overheads need to be improved.

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86, 5188 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, Phys. Rev. Lett. (to be published), quant-ph/0402005]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which nondeterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space. We expect these theorems to have a variety of applications in other areas of quantum-information science.